The cause of death in both cases was tear gas canisters aimed directly at the head, the sources said.
One protester was killed near Sinak bridge and the other near the adjacent Ahrar bridge, police said.
Hospital sources said some of the wounded protesters had injuries sustained from live ammunition and others were wounded by rubber bullets and tears gas canisters.
One killed, 200 injured in Baghdad anti-gov't protests
More than 300 people have been killed since the start of mass unrest in Baghdad and southern Iraq in early October, the largest demonstrations since the fall of Saddam Hussein in 2003.
The protests are an eruption of public anger against a ruling elite seen as enriching itself off the state and serving foreign powers, especially Iran, as many Iraqis languish in poverty without jobs, healthcare or education.
The unrest has shattered the relative calm that followed the defeat of the militant Islamic State in 2017.
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